Factual error: Trevor - a Professor of Geology - boasts about having an article published in Scientific American, and that is not something any scientist would do. Scientific American is looked upon with slight disdain by the scientific community, considered to be a populist crowd pleaser. It is not even peer reviewed. Considering that he has just turned the geological and archaeological worlds on their heads he would have been better off publishing in Journal of Geological Research or Geology, both prestigious professional journals.
Factual error: Fitch, who professes qualifications in biology, genetics and biochemistry, says that they made Sil female because she's a natural predator and so she'd be more docile. He should retake his finals. In every single species of predator on earth - every single one - the females are the hunters, aggressors and killers. The males may be socially dominant but they are the 'docile' ones. There are no exceptions - and no human DNA was used to create Sil - they used synthetic DNA based on the instructions transmitted to them.
Factual error: Listening to a radio broadcast, live, since no other indication is given, Joe Louis is completing the 12th round of a fight. This is December 6, 1941. Joe's last fight of 1941 occurred in September, his next fight was January 1942. (00:00:10)
Other mistake: In the slaughterhouse scene, after Harrigan has injured the Predator with his shotgun and Keyes reappears, the Predator throws its disc, and severs Keyes in half at the waist. We see his legs flop to the ground, and blood pour from above, but his upper half (torso, backpack and weaponry) mysteriously remain hovering out of sight. (01:21:50)
Continuity mistake: On the ferry, Rachel wears the purple/pink camouflage hoodie over her orange knit sweater with the colorful stripe sleeves, as usual. Now this is where things become strange. In the first shot as the trio come ashore, she is only wearing her orange sweater, she is not wearing the purple/pink hoodie - note the clear lack of fur hood. In the very next shot as they climb a bit more and then rest, Rachel is wearing the purple/pink hoodie - note the hood, but now it's on under her orange sweater. In the underwater shots she is also wearing it under the orange sweater. (This odd mistake has absolutely nothing to do with the very long wool cloak that Rachel wears in the next scene). (01:02:20 - 01:04:40)
Factual error: Amongst the essential parts of a nuclear weapon's detonation mechanism is a radioactive isotope of tritium, which has a half life of just 12 1/2 years. The tritium in every nuke on earth has to be replaced every ten years or so. This is by no means unusual; there are other perishable parts including detonators made of conventional explosives which would be completely inert after a thousand years. After lying dormant with no maintenance at all for that amount of time the nuclear weapons the 'Man-animals' find would be big shiny paperweights and not much else.
Continuity mistake: In the latter half of the movie, Picard looks at a picture of himself from his days as a Starfleet Academy cadet while Beverly looks on too. This picture is actually the actor Tom Hardy (Shinzon, Picard's clone) and he appears with a completely bald/shaved head. Showing Picard bald as a cadet completely contradicts the TNG series. In the TNG episode 'Tapestry', a flashback set in 2327 (the year Picard graduated from the Academy), Picard is shown with a full head of hair. Also, in the TNG episode 'Violations', a flashback set in 2354 shows Picard with a partial head of hair when he takes Beverly to see her dead husband Jack's body. (00:46:25)
Visible crew/equipment: When C-3PO is on the conveyor belt, if you look in the reflection in his head you can see the camera crew.
Continuity mistake: When the Senator is about to be sacrificed, the cloth on her mouth immediately disappears for a split second. (01:29:35)
Deliberate mistake: When MIB agents exit the lift to get into the main hall of the MIB Office, the lift opens halfway up the wall and they need to go down a little platform. But when K and J return during the lockdown and face the trashcan with guns, the lift opens at floor level, so it can be conveniently peppered with bullets. (01:02:05)
Revealing mistake: When Amidala and Anakin are eating and he cuts her a piece of the fruit and "floats" it back to her, the bite appears in the fruit a split second before she actually eats it. [This appears to be fixed in rereleased versions]. (00:53:40)